# What percent of minimum wage should I save from today,if I expect a certain percent of the then minimum wage,as income from corpus,after retirement?

I am trying to evolve a simple formula or a thumb-rule (under assumptions) to answer the question " Am I saving enough for my retirement ? " or "How much should I save today ?". But, not in absolute terms. I wish to look at both my savings and my expected income as a percentage over the minimum wage of any given year.

For example, say, I want to live at 150% of the "then" minimum wage when I retire. In the example, I am assuming that 150% will provide for what I think are basic needs. If that's my goal, what multiple of the minimum wage should I save from now onwards, starting from age 40, retiring at age 60, expecting to live upto 75. (I am not looking for answer for this example, I am looking at the model).

Assume the following :

Assumptions : 1. The current minimum wage in my country is M.

1. I am in year A1, age G1.

2. I expect to retire in year A2, age G2. I expect to die at year A3, at age G3

3. Current Inflation Rate is R and will remain the same till my death.

4. Interest Rate is N. This is the annual interest rate, which my retirement corpus will fetch me, post retirement. Assume it will remain the same till my death.

5. The minimum wage in my country grows at the same rate as inflation.

6. When I retire, I expect to receive an annual income that is D times the then minimum wage. This factor, retirement desire as a function of the respective year's minimum wage, is assumed to be same till my death.

7. Ignore post-retirement earning potential.

8. A corpus that is expected to last till death, accounting for inflation, will provide excess income in the early years. Assume then, that excess income in year A will be utilized in year A+1, before expecting the corpus to fund the income for the year A+1.

9. Assume there are no other sources of income, including rental income etc.

10. Assume my salary and expenses will be able to support my savings readiness.

11. Assume post-retirement income is non-taxable.

The question is :

Main Question : How many times the current minimum wage (that year's minimum wage) should I save every year till my retirement, so that, for every year after retirmeent, I will get D times the minimum wage of that year as interest, essentially living off my corpus till my death ?

Side questions : I am assuming the inflation rate and the interest income rate are the (only) major determinants of this. What other major economic factor am I ignoring ?

I have considered medical expenses etc and ignored it. It's uncertain, and when trying to quantify, we could mark the expected income as a greater percentage of the minimum wage to provide for this. Ditto for spouse support, children needs etc, I am not too keen on considering those.

What would be the mathematical model, if any, for this ? (I am aware asking for math etc may be too much of an offshoot in this forum, but I am not too keen about this, so I have put that as a side question of additional interest. )

• The maths for this stuff is actually quite complicated, even with all the stuff you excluded, as you're into series' and iterative calculations. If you actually want to figure out how much to save, rather than the answer to your question, you could try some numbers in an online pension payout calculator, to see what pot gives you your target income, then try some numbers in an online compound interest calculator to see what you need to save monthly to get the required pot. – Michael Feb 1 '16 at 19:53
• The inflation appears to bake into the rate of return here. Have you tried using the Excel standard functions PV (to determine the constant dollar amount needed as present value on date A2 to pay out a function of local income until A3) and PMT (to determine the payments needed to achieve a future value of this amount on A2, between A1 and A2)? – user662852 Feb 1 '16 at 21:48
• You can ignore inflation. You just use an inflation adjusted return on investment figure, so if you assume 3% inflation and 7% return, then just use 4%. As I said though, you can't develop a simple mathematical formula for this, you can develop a formula to calculate the sum of money you have from saving a given amount each month or year for a given time with a given return... but calculating the amount that taken out for a given number of years whilst adding the return and deducting the payout..... that is an iterative calculation. You could do it in excel/office but it's not a formula. – Michael Feb 1 '16 at 22:26
• @Michael : Good point, using inflation-adjusted return rate. – Whirl Mind Feb 1 '16 at 22:57

Why not Excel? You want to calculate the present value of the retirement account on the retirement date:

=PV(APY/12,RetMonths,MinMonthlyIncome*WageMult,DeathBalance)

Then determine the series of payments between now and the retirement date to have this amount:

=PMT(APY/12,AccumMonths,0,RetirementDateNeed)

Name the cells, and start plugging in different wages, multipliers, annual percentage yields, etc. You can also use the ppmt and ipmt functions for your own interest about what portion would be earnings versus principal for any period.

So for example, with APY = 5%, 180 months of retirement, \$1600 monthly income in A2 dollars I need \$202,328.39 on A2. To get there with 200 months of accumulation earning 5%, I need to pay \$492.24 per month each month from A1 to A2.

A comment about inflation: This generally assumes a constant-dollar and I'm not sure I could do everything you're assuming around inflation such as have the accumulation payment grow by inflation rate. You may need to experiment here: you could set APY as return minus inflation rate for both phases. Or do a side calculation to boost the MinMonthlyIncome by inflation over the accumulation months to determine what you expect it to be on date A2, then drop it into the PV calculation. To be more conservative, use Return in the accumulation phase (PMT calculation) and (Return-Inflation) in retirement phase (PV calculation).